U.S. patent application number 11/190482 was filed with the patent office on 2006-02-02 for disk drive, positioning method for head, and servo system.
This patent application is currently assigned to Hitachi Global Storage Technologies. Invention is credited to Masashi Kisaka.
Application Number | 20060023342 11/190482 |
Document ID | / |
Family ID | 35731856 |
Filed Date | 2006-02-02 |
United States Patent
Application |
20060023342 |
Kind Code |
A1 |
Kisaka; Masashi |
February 2, 2006 |
Disk drive, positioning method for head, and servo system
Abstract
Embodiments of the invention compensate for repeatable run-out
errors without causing servo system instability. In one embodiment,
HDD has a peak filter on a feedback route of a servo system. The
peak filter is designed so that a rotating frequency of a magnetic
disk, the high-frequency components contained in the rotating
frequency and a peak match the rotating frequency and the
high-frequency components. Insertion of a required peak filter into
the servo system allows compensation for a repeatable run-out (RRO)
error due to an event such as a deviation from the roundness of a
track. Also, since a Nyquist diagram of the system satisfies
required characteristics, a repeatable run-out error may be
compensated for without causing instability of the servo system due
to use of the peak filter.
Inventors: |
Kisaka; Masashi; (Kanagawa,
JP) |
Correspondence
Address: |
TOWNSEND AND TOWNSEND AND CREW LLP
TWO EMBARCADERO CENTER, 8TH FLOOR
SAN FRANCISCO
CA
94111
US
|
Assignee: |
Hitachi Global Storage
Technologies
Amsterdam
NL
|
Family ID: |
35731856 |
Appl. No.: |
11/190482 |
Filed: |
July 26, 2005 |
Current U.S.
Class: |
360/77.04 ;
360/77.02; G9B/5.221 |
Current CPC
Class: |
G11B 5/59627
20130101 |
Class at
Publication: |
360/077.04 ;
360/077.02 |
International
Class: |
G11B 5/596 20060101
G11B005/596 |
Foreign Application Data
Date |
Code |
Application Number |
Jul 30, 2004 |
JP |
2004-224749 |
Claims
1. A disk drive with a servo system for conducting position control
of a head by use of the servo signal recorded on a recording disk,
the servo system comprising: a head position signal generator
configured to generate, from the servo signal read from the
recording disk, a head position signal associated with a position
of the head; a peak filter having a peak at each of a plurality of
frequencies, the peak filter compensating for a repeatable run-out
error; and a control signal output unit which, on the basis of the
head position signal, a reference signal, and an output of the peak
filter, outputs a control signal for a driving device for moving
the head; wherein, in a Nyquist diagram based on an open-loop
transfer function of the servo system, when: with regard to each of
all peaks of ".omega.k", except ".omega.=0", of the peak filter,
Z.sub.0 is a point (-1, 0), Z.sub.01 is a point of the open-loop
transfer function of the servo system at ".omega.k" in the case
where the peak filter is not present, and Z.sub.k is a point of the
open-loop transfer function of the servo system at ".omega.k" in
the case where the peak filter is present, the angle formed by a
straight line extending from the Z.sub.0 point toward the Z.sub.01
point and a straight line extending from the Z.sub.01 point toward
the Z.sub.k point is 90.degree. or less.
2. The disk drive according to claim 1, wherein the angle formed by
the straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and the straight line extending from the Z.sub.01
point toward the Z.sub.k point is 60.degree. or less.
3. The disk drive according to claim 1, wherein the angle formed by
the straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and the straight line extending from the Z.sub.01
point toward the Z.sub.k point is 45.degree. or less.
4. The disk drive according to claim 1, wherein the angle formed by
the straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and the straight line extending from the Z.sub.01
point toward the Z.sub.k point is 0.degree..
5. The disk drive according to claim 1, wherein each peak of the
peak filter matches an integer multiple of a rotating frequency of
the recording disk.
6. The disk drive according to claim 1, wherein: the recording disk
comprises a plurality of tracks each having an M number of servo
sectors; and the peak filter generates an output signal on the
basis of a sum of the output of the peak filter at an Mth previous
sector and the value obtained by multiplying, by a weighting
coefficient, the plurality of state variables input during movement
from a preset Nth previous sector to a current sector.
7. The disk drive according to claim 6, wherein each state variable
is a deviation signal based on a differential between the reference
signal and the head position signal.
8. The disk drive according to claim 6, wherein: each state
variable is a deviation signal based on a differential between the
reference signal and the head position signal; and the peak filter
is inserted between an output of the deviation signal and an input
of the control signal output unit.
9. The disk drive according to claim 6, wherein: each state
variable is a deviation signal based on a differential between the
reference signal and the head position signal; and the peak filter
takes the output of the deviation signal as an input, wherein an
output of the control signal output unit and the output of the peak
filter are added.
10. The disk drive according to claim 1, wherein: the recording
disk comprises a plurality of tracks each having an M number of
servo sectors; and the peak filter conducts processing based on the
following expression: u .function. ( n ) = u .function. ( n - M ) +
k = 0 N .times. w k .times. X .function. ( n - k ) [ Numeric
.times. .times. expression .times. .times. 1 ] ##EQU16## u: peak
filter output, M: number of servo sectors in one track, w:
previously set real number, X: state variable in the servo system,
and N: previously set natural number, where .SIGMA. is a sum of the
plural terms selected from "k=0 to N".
11. A disk drive with a servo system for conducting head position
control by use of the servo signals recorded on a recording disk,
the servo system comprising: a head configured to access the
recording disk having a plurality of tracks each including an M
number of servo sectors, the head reading the servo signals of each
servo sector; a peak filter that outputs a value based on a sum of
the value obtained by multiplying, by a weighting coefficient, the
plurality of state variables input during movement from a preset
Nth previous sector to a current sector, and the value output at an
Mth previous sector; and a control signal output unit which, on the
basis of head position signals associated with the positions of the
head that are determined from the servo signals of each servo
sector, a reference signal, and an output of the peak filter,
outputs a control signal for a driving device for moving the head;
wherein, in a Nyquist diagram based on an open-loop transfer
function of the servo system, when: with regard to each of all
poles ".omega.k", except ".omega.=0", of the peak filter, Z.sub.0
is a point (-1, 0), Z.sub.01 is a point of the open-loop transfer
function of the servo system at ".omega.k" in the case where the
peak filter is not present, Z.sub.k is a point of the open-loop
transfer function of the servo system at ".omega.k" in the case
where the peak filter is present, the angle formed by a straight
line extending from the Z.sub.0 point toward the Z.sub.01 point and
a straight line extending from the Z.sub.01 point toward the
Z.sub.k point is 90.degree. or less.
12. The disk drive according to claim 11, wherein the angle formed
by the straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and the straight line extending from the Z.sub.01
point toward the Z.sub.k point is 60.degree. or less.
13. The disk drive according to claim 11, wherein the angle formed
by the straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and the straight line extending from the Z.sub.01
point toward the Z.sub.k point is 45.degree. or less.
14. The disk drive according to claim 11, wherein: each state
variable is a deviation signal based on a differential between the
reference signal and the head position signal; and the peak filter
is inserted between an output of the deviation signal and an input
of the control signal output unit.
15. The disk drive according to claim 11, wherein: The disk drive
according to claim 11, wherein: each state variable is a deviation
signal based on a differential between the reference signal and the
head position signal; and the peak filter takes the output of the
deviation signal as an input, wherein an output of the control
signal output unit and the output of the peak filter are added.
16. The disk drive according to claim 11, wherein the peak filter
conducts processing based on the following expression: u .function.
( n ) = u ) .times. n - M ) + k = 0 N .times. w k .times. X
.function. ( n - k ) [ Numeric .times. .times. expression .times.
.times. 2 ] ##EQU17## u: peak filter output, M: number of servo
sectors in one track, w: previously set real number, X: state
variable in the servo system, and N: previously set natural number,
where, however, .SIGMA. is a sum of the plural terms selected from
"k=0 to N".
17. A method of head position control in a disk drive, intended to
conduct position control of a head by use of the servo signals
recorded on a recording disk, the method comprising: accessing the
recording disk that has a plurality of tracks each including an M
number of servo sectors; reading the servo signals of each servo
sector; and in accordance with the head position signals determined
from the servo signals of each servo sector, the head position
signals being associated with positions of the head, a reference
signal, and a value based on a sum of the value obtained by
multiplying, by a weighting coefficient, the plurality of state
variables input during movement from a preset Nth previous sector
to a current sector, and the output of the peak filter that is
generated at an Mth previous sector, providing an output of a
control signal for a driving device which moves the head; wherein,
in a Nyquist diagram based on an open-loop transfer function of the
servo system, when: with regard to all polar ".omega.k", except
".omega.=0", of the peak filter, Z.sub.0 is a point (-1, 0),
Z.sub.01 is a point of the open-loop transfer function of the servo
system at ".omega.k" in the case where the above-mentioned peak
filter is not present, and Z.sub.k is a point of the open-loop
transfer function of the servo system at ".omega.k" in the case
where the above-mentioned peak filter is present, the Z.sub.0 point
is present outside a curve extending from the neighborhood of the
Z.sub.01 point, through the Z.sub.k point, toward the Z.sub.01
point.
18. The method of head position control in a disk drive according
to claim 17, wherein the angle formed by a straight line extending
from the Z.sub.0 point, toward the Z.sub.01 point, and a straight
line extending from the Z.sub.01 point, toward the Z.sub.k point,
is 90.degree. or less.
19. A servo system for positioning, on a rotary body, an object to
be controlled, the servo system comprising: a servo signal reader
configured to read the servo signal recorded on the rotary body;
and a controller having a peak filter whose gains at each of plural
frequencies equal to integral multiples of a rotating speed of the
rotary body are equal to or greater than defined values, the
controller generating, in accordance with the servo signal, with a
reference signal, and with an output of the peak filter, a control
signal for controlling a position of the object to be controlled;
wherein, in a Nyquist diagram based on an open-loop transfer
function of the servo system, when with regard to all peaks of
".omega.k", except ".omega.=0", of the peak filter, Z.sub.0 is a
point (-1, 0), Z.sub.01 is a point of the transfer function of the
servo system at ".omega.k" in the case where the peak filter is not
present, and Z.sub.k is a point of the open-loop transfer function
of the servo system at ".omega.k" in the case where the peak filter
is present, the angle formed by a straight line extending from the
Z.sub.0 point toward the Z.sub.01 point and a straight line
extending from the Z.sub.01 point toward the Z.sub.k point is
90.degree. or less.
20. The servo system according to claim 19, wherein: the rotary
body comprises a plurality of tracks each having an M number of
servo sectors; and the peak filter generates an output signal on
the basis of a sum of the output of the peak filter at an Mth
previous sector and the value obtained by multiplying, by a
weighting coefficient, the plurality of state variables input
during movement from a preset Nth previous sector to a current
sector.
Description
CROSS-REFERENCES TO RELATED APPLICATIONS
[0001] This application claims priority from Japanese Patent
Application No. JP2004-224749, filed Jul. 30, 2004, the entire
disclosure of which is incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] The present invention relates to a disk drive, a positioning
method for a head, and a servo system. More particularly, the
invention relates to a disk drive for compensating for repetition
errors by means of a filtering process, and an associated
head-positioning method and servo system.
[0003] The devices that use various forms of media such as optical
disks and magnetic tapes, are known as data storage devices. Among
these devices, hard-disk drives (HDDs) have come into widespread
use as storage devices in computers, and are one type of storage
devices indispensable in current computer systems. In addition,
HDDs are not only used in computers; the excellent characteristics
of HDDs are increasingly expanding their applications such as the
removable memories used in dynamic image recording/reproducing
apparatus, car navigation systems, digital cameras, or other
products.
[0004] The magnetic disks used in HDDs each have multiple tracks
formed into the shape of a concentric circle, and address
information (servo information) and user data are stored onto each
track. A magnetic head formed of a thin-film element can read or
write data by accessing a desired region (address) in accordance
with the address information. The magnetic head is fixed to a
slider, and the slider is further fixed to a carriage capable of
oscillating. The carriage is oscillated by a voice coil motor
(VCM), and thus the magnetic head can move to a desired position on
the magnetic disk. The VCM is driven by a VCM driver, and the VCM
driver drives the VCM by supplying an electric current thereto
according to the control data sent from a controller.
[0005] As mentioned above, each track has a data region into which
data is stored, and a servo region into which servo signals are
stored. A track ID, servo sector IDs, burst patterns, and others
are stored as servo data into the servo region. The track ID and
the servo sector IDs identify the addresses of the track and the
servo sectors, respectively. The burst patterns contain information
on the relative position of the magnetic head with respect to the
track, and are used during track following. The burst patterns are
each an array of regions in which signals were stored radially onto
the disk at fixed intervals, and one burst pattern is constituted
by multiple banks of signal storage regions different from one
another in terms of phase.
[0006] Data reading from or writing onto the magnetic disk is
executed while the position of the magnetic head is being confirmed
by means of servo signals in a rotating condition of the magnetic
disk. The servo signals that have been read by the magnetic head
are computed by the controller. The value of the electric current
to be supplied to the VCM is determined from the relationship
between the current position of the magnetic head and the desired
position thereof. The controller creates a control signal DACOUT
for indicating the calculated electric current value, and supplies
the current to the VCM driver. In case of a deviation, the carriage
is driven to compensate for the deviation and the position of the
magnetic head is controlled.
[0007] The servo signals, although usually recorded on the magnetic
disk by use of a servo track writer, are not always recorded in
perfect round form since vibration or the like can occur during
recording. The particular error appears as repeatable run-out (RRO)
during track following. If the RRO is significant, a track
following error can result since the magnetic head (servo system)
cannot follow the RRO. When the frequency components of the
repeatable run-out error are limited, for example, if the run-out
is great only at the rotating frequency components of the disk, it
is known that the run-out can be compensated for by inserting a
filter with a peak at that frequency into the servo system (for
this method, refer to Patent Document 1 (Japanese Patent Laid-Open
No. Hei 08-328664), for example).
[0008] It is generally known that repeatable run-out can be
compensated for by integrating the state variables that have been
input in the past. Since the filter used in this method has
multiple peaks associated with the frequency of the repeatable
run-out error, the filter can remove all of the repeatable run-out
error components.
[0009] Patent Document 2 (Japanese Translation of PCT for Patent
Application No. 2002-544639) discloses a technology for removing
RRO components from a position error signal (PES), the deviation
between a head position signal and a target signal. Removal of the
RRO components from signal PES makes the magnetic head follow a
substantially round path, not the shape of the track. Since the
servo system operates independently of the RRO, it is possible to
prevent the occurrence of a track following error due to the
RRO.
BRIEF SUMMARY OF THE INVENTION
[0010] The technology of Patent Document 2, however, does not
enable track servo signals to be read if their recording pattern
deviates from the round track significantly in terms of shape. In
terms of control, it is also necessary to multiply PES by a
function having the zero point of a frequency equal to an integer
multiple of the rotating frequency of the disk. Accordingly, if a
disturbance synchronous with the rotating frequency exists, the
disturbance cannot be distinguished from RRO. Therefore, it becomes
virtually impossible for such a distance to be followed, which
results in a position error. Meanwhile, as mentioned above, RRO
components and a disturbance synchronous with the rotating
frequency can be removed by inserting a required peak filter into
the servo system. The insertion of the peak filter, however, is
most likely to make the servo system unstable. If the system
becomes unstable, the head cannot stay at the same position and
thus becomes impossible to follow the track. For example, in the
technology of Patent Reference 1, selection of a phase term is
likely to result in the system becoming unstable. Also, the
small-gain theorem is generally known as a sufficient requirement
for stabilizing the system. This theorem, however, is only an
abstract theorem defining a general sufficient requirement for
stabilization, and does not specifically indicate a designing and
calculating method relating to a system which satisfies the
sufficient requirement. For example, the peak filter required for
system design, or a more specific servo system including this peak
filter is not described. During actual system design, therefore, it
is necessary to determine such characteristics of a peak filter and
specific servo system including the peak filter that do not cause
system instability.
[0011] The present invention was made with the above circumstances
as the background, and a feature of the invention is to enable RRO
to be followed in a servo system without making the servo system
unstable.
[0012] A first embodiment of the present invention is a disk drive
with a servo system for conducting position control of a head by
use of the servo signal recorded on a recording disk. In this disk
drive, the servo system is further divided into: a head position
signal generator (for example, a servo position signal generator
231) that generates, from the servo signal read from the recording
disk, a head position signal associated with the head position; a
peak filter (for example, a peak filter 234) that has a peak at
multiple frequencies and compensates for repeatable run-out; and a
control signal output unit (for example, a combination of an adding
element 236 and a servo controller 235) outputs a control signal
for a driving device which moves the head in accordance with the
head position signal, a reference signal (for example, a target
position signal) and an output of the peak filter; wherein, in a
Nyquist diagram based on an open-loop transfer function of the
servo system, when with regard to all peaks of ".omega.k", except
".omega.=0", of the peak filter, Z.sub.0 is a point (-1, 0),
Z.sub.01 is a point of the open-loop transfer function of the servo
system at ".omega.k" in the case where the above-mentioned peak
filter is not present, and Z.sub.k is a point of the open-loop
transfer function of the servo system at ".omega.k"0 in the case
where the above-mentioned peak filter is present, the angle formed
by a straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and a straight line extending from the Z.sub.01
point toward the Z.sub.k point is 90 degrees or less. The servo
system satisfies the above conditions, and this enables
compensation for RRO. Also, the stability of the system may be
obtained since the angle formed by the straight lines from the
Z.sub.01 point toward the Z.sub.k point is 90 degrees or less.
[0013] The angle formed by the straight line extending from the
Z.sub.0 point toward the Z.sub.01 point and the straight line
extending from the Z.sub.01 point toward the Z.sub.k point is
preferably 60 degrees or less. The angle formed by the straight
line extending from the Z.sub.0 point toward the Z.sub.01 point and
the straight line extending from the Z.sub.01 point toward the
Z.sub.k point is further preferably 45 degrees or less. The
stability of the system may be achieved by ensuring phase margins
in this manner while suppressing a processing load in accordance
with the above conditions.
[0014] In specific embodiments, the angle formed by the straight
line extending from the Z.sub.0 point toward the Z.sub.01 point and
the straight line extending from the Z.sub.01 point toward the
Z.sub.k point is preferably 0 degree. The stability of the servo
system may be further enhanced under this condition. Alternatively,
it is preferable that each peak of the peak filter should agree
with an integer multiple of a rotating frequency of the recording
disk. Thus, more reliable compensation for RRO becomes
possible.
[0015] It is preferable that the recording disk should include
multiple tracks each having an M number of servo sectors, and that
the peak filter should generate an output signal based on a sum of
the output which the peak filter generates at an Mth previous
sector, and the value obtained by multiplying, by a weighting
coefficient, the multiple state variables input during movement of
the head from a preset Nth previous sector to a current sector. It
is possible, by providing this process, to easily realize a peak
filter having a peak at a frequency equal to an integer multiple of
the rotating frequency.
[0016] As an example, the above-mentioned recording disk should
include multiple tracks, each having an M number of servo sectors,
and the peak filter should execute processing based on the
following expression: u .function. ( n ) = u .function. ( n - M ) +
k = 0 N .times. w k .times. .times. X .function. ( n - k ) [
Numeric .times. .times. expression .times. .times. 3 ] ##EQU1##
where u: peak filter output, M: number of servo sectors in one
track, w: previously set real number, X: state variable in the
servo system, and N: previously set natural number. However,
.SIGMA. is the sum calculated for the multiple terms that were
selected from "k=0 to N". The above state variable may be a
deviation signal based on the differential between the foregoing
reference signal and the foregoing position signal.
[0017] The above state variable may be a deviation signal based on
the differential between the foregoing reference signal and the
foregoing position signal, and the peak filter may be an element
inserted between an output of the foregoing deviation signal and an
input of the foregoing control signal output unit. Alternatively,
the above state variable may be a deviation signal based on the
differential between the foregoing reference signal and the
foregoing position signal, and the peak filter may take the output
of the foregoing deviation signal, as an input, and an output of
the foregoing control signal output unit and the output of the peak
filter, as an addition.
[0018] A second embodiment of the present invention is a disk drive
with a servo system for conducting position control of a head by
use of the servo signals recorded on a recording disk. In this disk
drive, the servo system is further divided into: a head that
accesses the recording disk having multiple tracks each including
an M number of servo sectors, and reads servo signals associated
with each servo sector; a peak filter that outputs a value based on
the sum of the value obtained by multiplying, by a weighting
coefficient, the multiple state variables (for example, PES) that
were input during movement of the head from the previously set Nth
previous sector to the current sector, and the output of the peak
filter that is generated at the Mth previous sector; and a control
signal output unit which, in accordance with head position signals
associated with the positions of the head that are determined from
the servo signals of each servo sector, a reference signal, and the
output of the peak filter, outputs a control signal for a driving
device which moves the head; wherein, in a Nyquist diagram based on
an open-loop transfer function of the servo system, when with
regard to all peaks of ".omega.k", except ".omega.k=0", of the peak
filter, Z.sub.0 is a point (-1, 0), Z.sub.01 is a point of the
open-loop transfer function of the servo system at ".omega.k" in
the case where the above-mentioned peak filter is not present, and
Z.sub.k is a point of the open-loop transfer function of the servo
system at ".omega.k" in the case where the above-mentioned peak
filter is present, the angle formed by a straight line extending
from the Z.sub.0 point toward the Z.sub.01 point and a straight
line extending from the Z.sub.01 point toward the Z.sub.k point is
90 degrees or less. The servo system satisfies the above
conditions, and this enables compensation for RRO without making
the system unstable.
[0019] The angle formed by the straight line extending from the
Z.sub.0 point toward the Z.sub.01 point and the straight line
extending from the Z.sub.01 point toward the Z.sub.k point is
preferably 60 degrees or less. The angle formed by the straight
line extending from the Z.sub.0 point toward the Z.sub.01 point and
the straight line extending from the Z.sub.01 point toward the
Z.sub.k point is further preferably 45 degrees or less. The
stability of the system may be achieved by ensuring phase margins
in this manner while suppressing a processing load in accordance
with the above conditions.
[0020] The above state variable may be a deviation signal based on
the differential between the foregoing reference signal and the
foregoing position signal. The peak filter may be an element
inserted between an output of the foregoing deviation signal and an
input of the foregoing controller. Alternatively, the above state
variable may be a deviation signal based on the differential
between the foregoing reference signal and the foregoing position
signal, and the peak filter may take the output of the foregoing
deviation signal, as an input, and an output of the foregoing
controller and the output of the peak filter, as an addition.
[0021] As an example, the above-mentioned peak filter should
execute processing based on the following expression: u .function.
( n ) = u .function. ( n - M ) + k = 0 N .times. w k .times.
.times. X .function. ( n - k ) [ Numeric .times. .times. expression
.times. .times. 4 ] ##EQU2## where u: peak filter output, M: number
of servo sectors in one track, w: previously set real number, X:
state variable in the servo system, and N: previously set natural
number. However, .SIGMA. is the sum calculated for the multiple
terms that were selected from "k=0 to N".
[0022] A third embodiment of the present invention is a method of
head position control in a disk drive, intended to conduct position
control of a head by use of the servo signals recorded on a
recording disk. This method includes: accessing the recording disk
having multiple tracks which each include an M number of servo
sectors; reading servo signals associated with each servo sector;
and, in accordance with three factors, (1) head position signals
associated with the positions of the head that are determined from
the servo signals of each servo sector, (2) a reference signal, and
(3) a value based on the sum of the value obtained by multiplying,
by a weighting coefficient, the multiple state variables that were
input during movement of the head from the preset Nth previous
sector to the current sector, and the output of the peak filter
that is generated at the Mth previous sector, providing an output
of a control signal for a driving device which moves the head;
wherein, in a Nyquist diagram based on an open-loop transfer
function of the servo system, when with regard to all polar
".omega.k", except ".omega.k=0", of the peak filter, Z.sub.0 is a
point (-1, 0), Z.sub.01 is a point of the open-loop transfer
function of the servo system at ".omega.k" in the case where the
above-mentioned peak filter is not present, and Z.sub.k is a point
of the open-loop transfer function of the servo system at
".omega.k" in the case where the above-mentioned peak filter is
present, the Z.sub.0 point is present outside a curve extending
from the neighborhood of the Z.sub.01 point through the Z.sub.k
point toward the Z.sub.01 point. According to the present
embodiment, a peak filter that efficiently compensates for RRO by
using both the output value generated at the Mth previous sector,
and the value obtained by multiplying the multiple state variables
by the weighting coefficient, may be constructed in the disk drive.
Also, the transfer function satisfies the above conditions and this
enables system stability to be obtained. In terms of the ease in
system stability design, it is preferable that the angle formed by
a straight line extending from the Z.sub.0 point toward the
Z.sub.01 point and a straight line extending from the Z.sub.01
point toward the Z.sub.k point be set to have a value of 90 degrees
or less.
[0023] A fourth embodiment of the present invention is a servo
system for positioning, on a rotary body, an object to be
controlled, wherein the servo system includes: a servo signal
reader for reading the servo signals recorded on the rotary body;
and a controller having a peak filter whose gains at each of
multiple frequencies equal to integral multiples of a rotational
speed of the rotary body are equal to or greater than defined
values, the controller generating a control signal for controlling
a position of the object to be controlled, in accordance with the
servo signals read above, a reference signal, and an output of the
peak filter; wherein, in a Nyquist diagram based on an open-loop
transfer function of the servo system, when with regard to each of
all peaks of ".omega.k", except ".omega.=0", of the peak filter,
Z.sub.0 is a point (-1, 0), Z.sub.01 is a point of the transfer
function of the servo system at ".omega.k" in the case where the
above-mentioned peak filter is not present, and Z.sub.k is a point
of the open-loop transfer function of the servo system at
".omega.k" in the case where the above-mentioned peak filter is
present, the angle formed by a straight line extending from the
Z.sub.0 point toward the Z.sub.01 point and a straight line
extending from the Z.sub.01 point toward the Z.sub.k point is 90
degrees or less. The servo system satisfies the above conditions,
and this enables compensation for RRO without making the system
unstable.
[0024] Preferably, the foregoing rotary body includes multiple
tracks each having an M number of servo sectors, and the foregoing
peak filter generates an output signal based on the sum of the
output of the peak filter that is generated at the Mth previous
sector, and the value obtained by multiplying, by a weighting
coefficient, the multiple state variables that were input during
movement from the preset Nth previous sector to the current sector.
It is possible, by providing this process, to easily realize a peak
filter having a peak at a frequency equal to an integer multiple of
the rotating frequency.
[0025] According to the present invention, RRO may be followed
without the instability of the servo system being caused.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] FIG. 1 is a block diagram showing a schematic configuration
of the hard-disk drive according to an embodiment of the present
invention.
[0027] FIG. 2 is a block diagram showing a configuration of the
servo system according to an embodiment of the present
invention.
[0028] FIG. 3 is a block diagram showing another configuration of
the servo system according to another embodiment of the present
invention.
[0029] FIG. 4 is a flowchart that shows process flow of the servo
system according to an embodiment of the present invention.
[0030] FIGS. 5A, 5B and 5C show Nyquist diagrams of open-loop
transfer functions of the servo system according to an embodiment
of the present invention.
[0031] FIG. 6 shows poles of the open-loop transfer functions of
the servo system according to an embodiment of the present
invention.
[0032] FIG. 7 is a Nyquist diagram showing the conditions that the
open-loop transfer functions of the servo system according to the
present embodiment satisfy.
[0033] FIGS. 8A and 8B are other Nyquist diagrams showing the
conditions that the open-loop transfer functions of the servo
system according to the present embodiment satisfy.
[0034] FIG. 9 is yet another Nyquist diagram showing the conditions
that the open-loop transfer functions of the servo system according
to the present embodiment satisfy.
DETAILED DESCRIPTION OF THE INVENTION
[0035] An embodiment that may be applied to the present invention
is described below. The following description relates to an
embodiment of the present invention, and the invention is not
limited to/by the embodiment described below. For the brevity and
clarity of description, the following description and drawings are
omitted and simplified as appropriate. Also, that each element of
the following embodiment may be easily modified, added, and
transformed within the scope of the present invention will be
understood by persons skilled in the art. In each drawing, the same
reference numeral is assigned to the same element, and for the
brevity and clarity of description, overlapped description is
omitted as required.
[0036] A hard-disk drive (HDD) of the present embodiment has a peak
filter on a feedback route of a servo system. The peak filter is
designed so that gains at a rotating speed of a magnetic disk and
in the high-frequency components contained in the rotating speed
take a defined value or more, and especially designed so that the
rotating speed, its high-frequency components, and a peak match.
Insertion of a required peak filter into the servo system allows
compensation for a repeatable run-out (RRO) error due to an event
such as a deviation from roundness of a track. Also, use of the
peak filter having required characteristics allows compensation for
a repeatable run-out error without causing instability of the servo
system due to peak filtering.
[0037] A total configuration of the HDD in which the servo system
is to be mounted is outlined to describe the servo system according
to the present embodiment. FIG. 1 is a block diagram showing a
schematic configuration of an HDD 1 according to the present
embodiment. The HDD 1 has, in its frame 10, a magnetic disk 11 that
is an example of a rotary disk (recording disk), a head element
section 12 that is an example of a head, arm electronics (AE) 13, a
spindle motor (SPM) 14, and a voice coil motor (VCM) 15. The HDD 1
also has a circuit board 20 fixed to the outside of the frame 10.
The circuit board 20 has, thereon, a read/write channel (R/W
channel) 21, a motor driver unit 22, a hard-disk controller
(HDC)/MPU integrated circuit (HDC/MPU) 23, and a RAM 24. These
constituent elements are only an example; for instance, they may
also be mounted in one chip.
[0038] Data to be written from an external host (not shown) is
received by the HDC/MPU 23 and then written onto the magnetic disk
11 via the R/W channel 21 and the AE 13 by the head element section
12. In addition, the data stored within the magnetic disk 11 is
read out by the head element section 12, and the thus-read data is
output from the HDC/MPU through the AE 13 and the R/W channel 21 to
the external host.
[0039] Next, the constituent elements of the HDD 1 are described
below. Driving mechanisms of the magnetic disk 11 and of the head
element section 12 are outlined first. The magnetic disk 11 is
fixed to a rotating shaft of the SPM 14. The SPM 14 is driven by
the motor driver unit 22, and the SPM 14 rotates the magnetic disk
11 at a required speed. The magnetic disk 11 has, on both sides, a
recording surface for recording data, and head element sections 12
associated with each recording surface. Each head element section
12 is fixed to a slider (not shown). Also, the slider is fixed to a
carriage (not shown). The carriage is fixed to the VCM 15, and
oscillates to move the slider and the head element section 12
radially on a surface of the magnetic disk 11. The head element
section 12 may thus access a desired region.
[0040] Typically, a recording head for converting electrical
signals into a magnetic field according to the data stored onto the
magnetic disk 11, and a reproducing head for reconverting the
electrical signals into the magnetic field applied from the
magnetic disk 11, are integrally formed at the head element section
12. The number of magnetic disks 11 may be one or more, and a
recording surface may be formed only on one side of each magnetic
disk 11 or on both sides thereof. Additionally, the servo system of
the present invention may be applied to a device having either the
reproducing or recording head only.
[0041] Next, circuit blocks are described below. The AE 13 selects,
from multiple head element sections 12, one head element section 12
to be subjected to data accessing, preamplifies with a fixed gain
the signal reproduced by the selected head element section 12, and
sends the reproduced signal to the R/W channel 21. The AE 13 also
sends the recording signal received from the R/W channel 21, to the
selected head element section 12.
[0042] The R/W channel 21 performs a writing process on the data
acquired from the host. During the writing process, the R/W channel
21 modulates into codes the write data supplied from the HDC/MPU
23, further converts the code-modulated write data into write
signals (electric currents), and supplies the data to the AE 13.
Also, the R/W channel 21 performs a reading process when assigning
data to the host. During the reading process, the R/W channel 21,
after receiving a reading signal from the AE 13, amplifies this
signal to obtain fixed amplitude, then extracts data from the
acquired reading signal, and decodes the data. The data thus read
out includes user data and servo data. The decoded reading data is
assigned to the HDC/MPU 23.
[0043] The HDC/MPU 23 is a circuit having the HDC and the MPU
integrated into one chip. The MPU operates in accordance with the
microcodes loaded into the RAM 24, and executes necessary data
processing in addition to total HDD 1 control such as positioning
control of the head element section 12, interface control, and
defect management. As the HDD 1 starts operating, the data required
for control and for data processing, in addition to the microcodes
operating on the MPU, is loaded from the magnetic disk 11 or a ROM
(not shown) into the RAM 24.
[0044] Data that is read out by the R/W channel 21 includes servo
data as well as user data. The HDC/MPU 23 conducts the positioning
control of the head element section 12 that uses the servo data. A
control signal (digital signal) from the HDC/MPU 23 is output to
the motor driver unit 22. The motor driver unit 22 supplies a
driving current to the VCM 15 according to a particular level of
the control signal.
[0045] Next, the servo system in the HDD 1 of the present
embodiment is described below. FIG. 2 is a block diagram showing a
configuration of the servo system of the present embodiment. The
RIW channel 21 includes a servo channel 211 that extracts a servo
signal from the signal output from the AE 13. The HDC/MPU 23
includes: a servo position signal generator 231 that generates a
servo position signal; a target position setter 232 that sets a
target position for the head element section 12; a position error
signal generator 233 that generates a position error signal (PES)
on the basis of the servo position signal and the target position
signal sent as a reference signal from the target position setter
232; a peak filter 234; and a servo controller 235 that outputs to
the motor driver unit 22 a digital control signal (DACOUT) for
controlling the VCM 15 (i.e., controlling the amount of current of
the VCM 15).
[0046] Each internal constituent element of the HDC/MPU 23 may be
realized in a hardware configuration or by using the microcodes
operating on the MPU. An appropriate hardware/software
configuration is selected according to design. Logic blocks for
executing necessary processing may also be mounted in any hardware
configuration by appropriate design.
[0047] Servo signals are recorded radially on the magnetic disk 11.
Each of the servo signals (servo reproduction signals) includes a
gap, servo AGC (Auto Gain Control) information, a servo address,
and a burst pattern. The gap absorbs timing errors due to factors
such as changes in rotating speed. The servo AGC information is
used to determine the servo signal gain to be subjected to AGC. The
servo address includes a cylinder ID, servo sector numbers, and
other address information. The burst pattern is used to conduct
tracking control (track following), or the like, of the head
element section 12 by digitizing changes in the amplitude or other
factors of the particular reproduction signal.
[0048] Each servo signal on the magnetic disk 11 is read out from
the head element section 12, amplified by the AE 13, and input to
the servo channel 211. The servo channel 211 becomes active at a
required control period and acquires the servo signal from the AE
13. The servo channel 211, after acquiring an analog servo signal
from the AE 13, also converts the analog signal into digital form
at a required sampling frequency. The servo channel 211 further
decodes a servo address from the A/D-converted signal. The address
that has thus been decoded and an A/D-converted burst signal are
transferred to the servo position signal generator 231.
[0049] On the basis of the servo signal sent from the servo channel
211, the servo position signal generator 231 generates a servo
position signal that indicates a current position of the head
element section 12. The target position setter 232 outputs a target
position signal that indicates a target position to which the head
element section 12 is to move. The position error signal generator
233 compares the servo position signal and the target position
signal and generates a signal (PES) that indicates a size and
direction of a deviation of the current position with respect to
the target position. Signal PES indicates how far the head element
section 12 is deviated from the target position internally or
externally in a radial direction of the magnetic disk 11.
[0050] Signal PES that was generated by the position error signal
generator 233 is input to the peak filter 234. The peak filter 234
has multiple peaks at frequencies equal to integer multiples
(.times.1 included) of the rotating frequency of the magnetic disk
11. When analog signals from the AE 13 are converted into digital
signals, the peak filter 234 has peaks at all frequencies less than
Nyquist frequency equal to integer multiples of the rotating
frequency.
[0051] Signal PES from the position error signal generator 233, and
an output from the peak filter 234 are additively integrated by the
adding element 236. The signal thus generated by the adding element
236 is then input to the servo controller 235. The servo controller
235 generates DACOUT, a control signal for controlling the VCM 15,
based on signal PES and on the output signal of the peak filter
234. The DACOUT signal, an output signal to DAC of the motor driver
unit 22, is input to the motor driver unit 22, which then
DA-converts DACOUT and supplies a current of a required value to
the VCM 15.
[0052] As described above, in the servo system of the present
embodiment, the servo controller 235 generates a control signal for
the VCM 15, based on the signal PES from the position error signal
generator 233 and on the output signal from the peak filter 234
which filters signal PES. The peak filter 234 has multiple peaks,
and it also has a gain equal to or greater than a defined value, at
a frequency equal to an integer multiple of the rotating frequency.
In the present example, in particular, the peak filter 234 in a
preferred embodiment has a peak at multiple frequencies equal to
integer multiples of the rotating frequency. Repeatable run-out
errors in servo signals may be effectively compensated for by
inserting the peak filter 234 into a feedback circuit of the servo
system.
[0053] In this case, the inserting position of the peak filter is
not limited to the section between the output of the position error
signal generator 233 and the input of the servo controller 235.
Instead of the above, as shown in FIG. 3, a peak filter 237 is
insertable between the output section of the signal PES and the
input section to DACOUT. The servo controller 235 generates a
control signal based on the signal PES received from the position
error signal generator 233. Also, signal PES from the position
error signal generator 233 is input to the peak filter 237. The
output signal from the peak filter 237 and the control signal from
the servo controller 235 are input to an adding element 238, and
the signal thus generated by the adding element 238 is then input
as control signal DACOUT to the motor driver unit 22.
[0054] As described above, repeatable run-out errors may be
compensated for by inserting the required peak filter 234 or 237
into the feedback route of the servo system. Characteristics of the
peak filters 234 and 237 and of the servo system including the peak
filter are described below. The peak filter in the present
embodiment calculates the sum of the peak filter output generated
at the Mth previous sector (M is the number of servo sectors in one
track, and is equivalent to a previous full turn of the head), and
the value obtained by multiplying, by a weighting coefficient, the
state variables of selected multiple servo sectors that were read
before movement to the current servo sector. That is to say, the
peak filter executes the arithmetic process conforming to the
following numeric expression: [ Numeric .times. .times. expression
.times. .times. 5 ] u .function. ( n ) = u .function. ( n - M ) + k
= 0 N .times. w k .times. .times. X .function. ( n - k ) ( 1 )
##EQU3## In the above numeric expression (1), "u" is a peak filter
output, M is the number of servo sectors in one track, "w" is a
previously set real number, X is a state variable in the servo
system, and N is a previously set natural number. However, .SIGMA.
in the above expression is the sum calculated for the multiple
terms that were selected from "k=0 to N". The number of multiple
terms selected or which term is to be selected is determined by
design. The signal PES or the output signal DACOUT to the motor
driver unit 22 is usable as the state variable X.
[0055] Described below is an example of an element functioning as
the peak filter 234 or 237 by integrating the filter output
generated at the Mth previous sector, and the required number of
state variables from the M number of previous sectors (i.e., at the
end of the previous full turn of the head), especially, error
component PES. That is, in the foregoing description, signal PES is
equivalent to the state variable X. The peak filter 234 or 237
executes arithmetic processing defined by the following expression:
[ Numeric .times. .times. expression .times. .times. 6 ] u
.function. ( n ) = U .function. ( n - M ) + k = 0 k .times. w k
.times. .times. PES .function. ( n - ( M - k ) ) ( 2 ) ##EQU4##
where K is a natural number predetermined by design. Also, .SIGMA.,
unlike that of numeric expression (1), means the sum of each term
from "k=0" to "K".
[0056] Z-transformation of these numeric expressions is represented
as "f(z)/(z.sup.M-1)", in which "f(z)" is a required function of
"z", and this transfer function has a pole at "z" which satisfies
"z.sup.M-1". As described above, the peak filter 234 or 237 has a
peak at all places of the rotating frequency of the magnetic disk
11, and of higher-order frequencies, and may therefore remove
repeatable run-out error components at all frequencies.
[0057] The peak filter 234 or 237 that executes arithmetic
processing represented by above numeric expression (2) is to
determine an output value based on the sum of the filter output
generated at the Mth previous sector, and the value obtained by
multiplying, by a weighting coefficient, state variables associated
with multiple sectors from the Mth previous sector to the current
sector. Signals PES [PES (n-M) to PES (n-M+k)] associated with
multiple successive sectors from the Mth previous sector to the
current sector are used in the example of numeric expression (2).
However, as shown in numeric expression (1), what section of the
set of signals PES associated with the multiple sectors from the
Mth previous sector to the current sector is to be used is
determined by design. For example, signals associated with a
definite number of previous sectors [PES (n) to PES (n-N)] from the
current sector may be used, which is, in integration of the above
expression, equivalent to a change of "(M-k)" to "k" in the
equation (2). The servo system has determined control signal DACOUT
by digital processing, and of higher-order frequencies than the
rotating frequency, only those lower than the Nyquist frequency
become a problem.
[0058] A peak filter 234 or 237 having a value of K=3 in a system
of M>3 is shown below as an example of an element which obeys
above expression (2). The peak filter 234 executes arithmetic
processing that obeys the following numeric expression (3): [
Numeric .times. .times. expression .times. .times. 7 ] u .function.
( n ) = u .function. ( u - m ) + w M - 3 .times. .times. PES
.function. ( n - M + 3 ) + W M - 2 .times. .times. PES .function. (
n - M + 2 ) + w M - 1 .times. .times. PES .function. ( n - M + 1 )
+ w M .times. .times. PES .function. ( n - M ) ( 3 ) ##EQU5## This
is equivalent to a case in which M>3 and f(z) are taken as
having assigned to a cubic polynomial. More specifically,
Z-transformation of above numeric expression (3) gives f(z) as
follows:
[0059] [Numeric Expression 8]
u(z)=z.sup.-mU(Z)+w.sub.M-3Z.sup.3-MPES(z)+.LAMBDA.+w.sub.Mz.sup.-M
PES(z) U(Z)=W.sub.M-3Z.sup.3+.LAMBDA.+w.sub.M)PES(z)/)z.sup.M-1)
f(Z)=w.sub.M-3Z.sup.3+w.sub.M-2Z.sup.2+w.sub.M-1Z-w.sub.M (4)
[0060] An example of processing in which the peak filter 234 that
conducts processing of numeric expression (3) is used in the system
of FIG. 2 is described below with reference to a flowchart of FIG.
4. After waiting for movement to a sector (i) in step S11, the
system acquires, in step S12, PES(n) that has been read at the
sector (i). The peak filter 234 uses acquired PES(n) to calculate
U(u) by conducting arithmetic processing shown in the numeric
expression of step S13. In step S14, an adding element 236 adds the
U(n) output of the peak filter 234 and PES(n), and then outputs
Y(n). In step S15, the servo controller 235 generates control
signal DACOUT from Y(n) and outputs the signal to the motor driver
unit 22.
[0061] It is necessary at this time to prevent the servo system
from being made unstable by the peak filter 234 that executes the
above arithmetic processing. Insertion of any peak filter is likely
to result in the system becoming unstable. To ensure servo system
stability, it is necessary to insert a peak filter of required
characteristics. To add state variables of the past as in the
present example, the number of terms (value of K) added in the peak
filter 234 or 237 and coefficients "w" of each term need to be
appropriately set so as to satisfy the required characteristics.
The peak filter 234 or 237 that maintains system stability, a
method of designing the servo system including this peak filter,
and the characteristics that the servo system and the peak filter
are to satisfy are described below.
[0062] The characteristics that the peak filter 234 or 237 is to
satisfy may be defined by using a Nyquist diagram. Take a transfer
function of the peak filter 234 or 237 as F(z), a transfer function
of the servo controller 235, as C(z), and a transfer function from
an output of the servo controller 235 to that of the servo position
signal generator 231, as P(z). Open-loop transfer function H1 in
the servo system of FIG. 2 is expressed as H1=PC(1+F), and
open-loop transfer function H2 in the servo system of FIG. 3 is
expressed as H2=P(C+F).
[0063] In a servo system not having an inserted peak filter 234 or
237, open-loop transfer function H is expressed by H3=PC. When "z"
changes from 0 to 2.pi. as shown in FIG. 5A, a Nyquist diagram
(vector locus) of this open-loop transfer function H3 (=PC) yields,
for example, such a curve looks as shown in FIG. 5B (this curve
only forms part of an example of a locus). In the system having the
inserted peak filter 234 or 237 of the present embodiment, a
Nyquist diagram of open-loop transfer function H1 or H2 changes,
for example, from the curve of H3, shown in FIG. 5B, to such a
curve as shown in FIG. 5C.
[0064] Since the peak filter 234 or 237 has a peak at each of
frequencies equal to integer multiples of the rotating frequency of
the magnetic disk 11, the Nyquist diagram changes in the
neighborhood of each frequency equal to integer multiples of the
rotating frequency. The vector locus at one frequency value (polar
value "Z.sub.0") generated by the peak filter 234 or 237 is shown
in FIG. 5C. In actuality, the Nyquist diagram changes in the
neighborhood of each frequency equal to integer multiples of the
rotating frequency.
[0065] Transfer function F of the peak filter 234 or 237 has, on a
unit circle, multiple poles "zi" equivalent to an integer-multiple
frequency ".omega.i" of the rotating frequency. When each such pole
is regarded as a stable pole, the system may be stabilized if the
number of times a vector locus generated by open-loop transfer
function H1 or H2 (or the transfer function of the peak filter 234,
237) circles a point of Z.sub.0(-1,0) on a complex plane is not
increased. In the example of FIG. 5C, the number of times the
vector locus circles the point of Z.sub.0(-1,0) is not increased.
At each frequency equal to integer multiples of the rotating
frequency, the system is stable when the above requirement is
satisfied.
[0066] The above requirement for stabilizing the system may be
derived from the principle of argument or from the Nyquist's
stability criterion that applies this principle to a control
system. According to the principle of argument, when the number of
zero points of a function Q(z) in a circumference C (i.e., the
number of "z" points at which H becomes zero) and the number of
poles of Q(z) (i.e., the number of "z" points at which 1/Q
diverges) are taken as Z and P respectively, and both include
duplication levels, the curve generated by duplicating the
circumference C by means of Q rotates through (P-Z) turns in a
forward direction (clockwise).
[0067] When a frequency changes from 0 to 2.pi., "z" of
z-transformation rotates through a full turn around a unit circle.
From Nyquist's stability criterion, when "z" rotates through a full
turn around the unit circle, the difference between the number of
zero points and that of poles, in the unit circle of a
characteristic equation [1+H(z)] of the system, is identified
according to how often H(z) circles a point of (-1, 0). When pole
positions are previously known, the number of poles in the unit
circle is identified from the number of rotations, and provided
that all zero points as many as determined by degree exist in the
unit circle, the system is stable.
[0068] In the present embodiment, transfer function F of the peak
filter 234 or 237 has multiple poles "zi" on a unit circle, and
each pole "zi" is regarded as a stable pole. That is, when transfer
function F is represented as [ Numeric .times. .times. expression
.times. .times. 9 ] F = f .function. ( z ) z M - 1 ( 5 ) ##EQU6##
the vector locus at each pole "zi" of the transfer function F of
the peak filter 234 is obtained by: [ Numeric .times. .times.
expression .times. .times. 10 ] F .function. ( zi ) = f .function.
( z ) z M - r ( from .times. .times. r < 1 .times. .times. to
.times. .times. r .fwdarw. 1 ) ( 6 ) ##EQU7## FIG. 6 shows one pole
"z0" on the unit circle, as an example. As shown in FIG. 6, in the
unit circle, pole "Z.sub.0" is calculated as a value (from r<1
to r.fwdarw.1) infinitely close to the unit circle.
[0069] If a pole is present inside the vector locus (unit circle)
of "z", in order for the system to be stable, it is necessary that
the number of rotations with respect to (-1, 0) of the open-loop
transfer function should not be changed by insertion of the peak
filter 234 or 237. In other words, it is necessary that as shown in
FIG. 5C, the number of rotations of H(z) with respect to (-1, 0)
should not be increased with respect to the locus of "z" on the
unit circle. The vector locus of 1/(z.sup.M-1) infinitely goes far
at the frequencies that satisfy z.sup.M=1. Therefore, even if the
vector locus starts from a point distant from (-1, 0), the system
is apt to become unstable since there is the possibility of the
locus approaching the point of (-1, 0). In the design method of the
present embodiment, the number of terms in the polynomial shown in
numeric expression (2) and coefficients "w" of each term are set so
that the peak filter 234 or 237 or the system including the filter
satisfies the above characteristics.
[0070] As described above, it is the requirement for stabilization
that the locus of H(z), generated by use of the peak filter 234 or
237, should not surround Z.sub.0(-1, 0). Here, for a central
frequency "zk" of the peak filter, take the value of a transfer
function (e.g., above-mentioned H3), in the case of the peak filter
234 or 237 not being inserted, as Z.sub.01, and the value of a
transfer function (e.g., above-mentioned H2 or H2), in the case of
the peak filter 234 or 237 being inserted, as Z.sub.k. As shown in
FIG. 7, on the straight line defined by points Z.sub.0 and
Z.sub.01, if point Z.sub.k is present on an opposite side to point
Z.sub.0 across point Z.sub.01, the transfer function in the case of
the peak filter 234 or 237 being inserted generates a vector locus
directed away from Z.sub.0. Accordingly, when Z.sub.k is present at
the position where the above requirement is satisfied, a stable
system may be reliably formed.
[0071] The transfer function of the peak filter 234 that satisfies
the requirement shown in FIG. 7 is described below taking the
composition (transfer function H1) of FIG. 2 as an example. The
following numeric expression is satisfied with reference to FIGS. 2
and 7:
[0072] [Numeric Expression 11]
Z.sub.k=PC(1+F)=Z.sub.01(1+F)=Z.sub.01+.lamda.(Z.sub.01-Z.sub.0)
.lamda.>0 (7) Hence: [ Numeric .times. .times. expression
.times. .times. 12 ] F = .lamda. .times. .times. Z 01 - Z 0 Z 01 (
8 ) ##EQU8## is the desirable transfer function of the peak filter
234.
[0073] A phase of the peak filter 234 may be specified as follows.
Here, the transfer function F of the peak filter 234 is expressed
as follows: [ Numeric .times. .times. expression .times. .times. 13
] F = f .function. ( z ) z M - 1 ( 9 ) ##EQU9## Consider the phase
at the following central frequency of a peak: [ Numeric .times.
.times. expression .times. .times. 14 ] z k = exp .function. ( j
.times. .times. .omega. 0 .times. k ) ( .omega. 0 .times. : .times.
.times. 2 .times. .times. .pi. M , k .times. : .times. .times.
integer .times. .times. from .times. .times. 1 .times. .times. to
.times. .times. M / 2 ) ( 10 ) ##EQU10## For calculation of an
angle of the transfer function F, substituting the denominator of
numeric expression (9) as follows
[0074] [Numeric Expression 15] z.sup.M-1z.sup.M-r (11) and then
calculating the convergence value obtained at the central frequency
by r.fwdarw.1 yields
[0075] [Numeric Expression 16]
.angle.F(z.sub.k).apprxeq..angle.f(z.sub.k) (12) at the central
frequency. In this numeric expression, .angle.F denotes the angle
of F. It follows from the relationship between numeric expressions
8 and 12 that:
[0076] [Numeric expression 17] .angle. .times. .times. f .function.
( z k ) = .angle. .times. .times. Z 01 - Z 0 Z 01 ( 13 )
##EQU11##
[0077] A stable system with an inserted peak filter 234 may be
constructed by determining function "f(z)" so that numeric
expression (13) should hold at the rotating frequency and all its
higher harmonics of the magnetic disk 11. Regarding a gain, a small
value, for example, may be assumed, in which case, the filter
operates in a narrow frequency band and exhibits desirable
characteristics. Although the phase of ".omega.=0" is not
determined by the above expression, the phase may be zero since
integer terms are stabilized only by NFB (Negative Feed Back).
[0078] Although a sufficiently stable system may be constructed by
making numeric expression (13) hold at the rotating frequency and
all its higher harmonics of the magnetic disk 11, the order of the
function "f(z)" needs to be increased to satisfy the above
requirement. Increasing the order makes arithmetic processing
complex and the circuit scale or computing time increase. To
construct a stable system, the above requirement is most
preferable. It is not required, however, that the above requirement
not always be satisfied to ensure system stability. Although system
stability decreases, provided that the peak filter 234 satisfies
the requirement shown below, the stability required of the system
may be satisfied.
[0079] When, with respect to a central frequency "k.omega.o" of the
peak filter 234, "k.omega.o+q" (q.fwdarw.0) yields an asymptotic
property, consideration of the vector locus generated by the
transfer function F of the peak filter 234 allows [ Numeric .times.
.times. expression .times. .times. 18 ] .angle. .times. .times. F
.function. ( k .times. .times. .omega. 0 + q ) = .angle. .times.
.times. f .function. ( z k ) z M - 1 ( 14 ) .times. = .angle.
.times. .times. f .function. ( z k ) e j .function. ( k .times.
.times. .omega. .times. .times. 0 + q ) M - 1 .times. = .angle.
.times. .times. f .function. ( z k ) j .times. .times. q .times.
.times. M .times. = .angle. .times. .times. F .function. ( k
.times. .times. .omega. 0 ) - .pi. 2 ##EQU12## to be obtained from
the relationship between numeric expression (12) and "j (imaginary
number)=exp(j.pi./2)". That is to say, the angle of the transfer
function F of the peak filter 234 in the neighborhood of the
central frequency "k.omega.o" is 90 degrees off with respect to the
angle of the transfer function F at the central frequency
"k.omega.o". FIG. 8 shows an extending direction of the vector
locus of open-loop transfer function H in the neighborhood of
"k.omega.o". In the neighborhood of "k.omega.o", the vector locus
of the open-loop transfer function H (the vector locus generated by
the open-loop transfer function F in the neighborhood of
"k.omega.o") extends from the neighborhood of Z.sub.01, in a
direction orthogonal to the line that connects Z.sub.01 and
Z.sub.k.
[0080] In order for the system to be stable, it is necessary that
the vector locus of the open-loop transfer function H should not
circle the point of Z.sub.0 (-1, 0) and that Z.sub.0 be present
outside the curve (locus) extending from a point in the
neighborhood of Z.sub.01 through Z.sub.k to another neighboring
point. This requirement is satisfied if, as shown in FIG. 8A, in a
direction orthogonal to the straight line that connects Z.sub.01
and Z.sub.k, the straight line extending from Z.sub.01 exists below
Z.sub.0, i.e., between Z.sub.0 and Z.sub.k. Conversely, the system
may become unstable if, as shown in FIG. 8B, the line extending
from Z.sub.01 exists above Z.sub.0 in the orthogonal direction to
the line that connects Z.sub.01 and Z.sub.k. The system may
therefore be stabilized if, as shown in FIG. 9, the angle ".phi."
formed by a straight line "c" extending from Z.sub.0 to Z.sub.01
and a straight line "a" extending from Z.sub.01 to Z.sub.k is 90
degrees or less. In other words, changing numeric expression (7)
into
[0081] [Numeric expression 19]
Z.sub.k=PC(1+F)=Z.sub.01(1+F)=Z.sub.01+.lamda.(Z.sub.01-Z.sub.0)e.sup.j.p-
hi. .lamda.>0 (15) and then calculating the angle at "k.omega.o"
of F yields: [ Numeric .times. .times. expression .times. .times.
20 ] .angle. .times. .times. F .function. ( z k ) = .angle. .times.
.times. ( Z 01 - Z 0 Z 01 + .PHI. ( 16 ) ##EQU13## If .phi. is 90
degrees or less, the system may be stabilized. Taking the right
side of numeric expression (13) as ".alpha.", enables the system to
be stabilized, provided that the following numeric expression (17)
is satisfied:
[0082] [Numeric expression 21]
|.phi.F(k.omega..sub.0)-.alpha.|.ltoreq.90.degree. (17)
[0083] However, it reduces system stability if the vector locus of
the open-loop transfer function H approaches Z.sub.0 (1, 0). In
addition, it is important that there be a phase margin in the servo
system. During the design of the servo system, it is preferable
that 30 degrees be set as the phase margin. Hence, it is preferable
that the angle ".phi." formed by the straight line "a" connecting
Z.sub.01 and Z.sub.k and the straight line "c" connecting Z.sub.0
and Z.sub.01 should be 60 degrees or less (|.angle.F
(k.omega.o)-.alpha.|.ltoreq./60 deg). Furthermore, the need may
arise for a peak width to be spread for faster convergence of the
peak filter. If that is the case, since original frequency
characteristics are affected, the phase margin of 30 degrees is
likely to decrease. It is therefore preferable that a greater phase
margin be reserved. Accordingly, further preferably, the angle
".phi." formed by the straight line "a" connecting Z.sub.01 and
Z.sub.k and the straight line "c" connecting Z.sub.0 and Z.sub.01
is 45 degrees or less (|.angle.F
(k.omega.o)-.alpha.|.ltoreq./45.degree.). These requirements are
satisfied at the rotating frequency of the magnetic disk 11 and at
all its higher harmonics ("k.omega.o"). On the straight line
defined by points Z.sub.0 and Z.sub.01, if point Z.sub.k is present
on an opposite side to point Z.sub.0, across point Z.sub.01, the
angle ".phi." is 0 degree. As described above, when conditional
expressions for angle are represented using simultaneous
inequalities, the number of terms for the peak filter 234 and
coefficients of each term may be determined using LMI (Linear
Matrix Inequalities). The peak filter 234 conducts a filtering
process in accordance with the values thus predetermined.
Description of LMI is omitted since it is a most commonly known
technology as described in, for example, Stephen Boyd, etc.,
"Linear Matrix Inequalities in System and Control Theory", 1994,
SIAM.
[0084] Although the above description has been given with the
open-loop transfer function H1 [PC (1+F)] as an example, system
stability may likewise be obtained under similar conditions by
using open-loop transfer function H2 [P (C+F)]. For open-loop
transfer function H, the following expression holds:
[0085] [Numeric expression 22]
Z.sub.k=P(C+F)=Z.sub.01+.lamda.(Z.sub.01-Z.sub.0) .lamda.>0 (18)
Therefore: [ Numeric .times. .times. expression .times. .times. 23
] F = .lamda. .times. .times. Z 01 - Z 0 ) P ( 19 ) ##EQU14## is a
most preferable transfer function of the peak filter 234. The angle
requirement in this case is: [ Numeric .times. .times. expression
.times. .times. 24 ] .angle. .times. .times. f .function. ( Z k ) =
.angle. .times. .times. Z 01 - Z 0 ) P ( 20 ) ##EQU15##
[0086] As described above, according to the HDD in the present
embodiment, it is possible to effectively compensate for RRO while
at the same time maintaining servo system stability. While, in the
present embodiment, the HDD may conduct data read and write
processes, the present invention may also be applied to a
reproduce-only device that conducts reproduction only. The
invention, although particularly useful for a magnetic disk storage
device, may be applied to other forms of storage devices such as an
optical storage device for optically processing stored data, or to
servo systems for other objects that are to be controlled.
[0087] It is to be understood that the above description is
intended to be illustrative and not restrictive. Many embodiments
will be apparent to those of skill in the art upon reviewing the
above description. The scope of the invention should, therefore, be
determined not with reference to the above description, but instead
should be determined with reference to the appended claims alone
with their full scope of equivalents.
* * * * *